SEOUL, Feb 12 (Reuters) - South Korea said on Monday it will try to arrange more reunions for families divided by the Korean War and seek to lower military tensions with North Korea as the first steps towards establishing grounds for a rare summit between the two Koreas.

The statement from the Ministry of Unification came after a high-level North Korean delegation concluded a three-day visit which included an invitation for South Korean President Moon Jae-in to travel to Pyongyang for talks.

“(The visit) shows North Korea’s will to improve inter-Korean ties is very strong and if needed it will take unprecedented and aggressive measures,” the ministry said.

The visit of the delegation, which included North Korean leader Kim Jong Un’s younger sister Kim Yo Jong, intrigued many in South Korea, but also met scepticism about the North’s sincerity and willingness to give up its pursuit of nuclear weapons.

“Although many Koreans are welcoming North Korea’s participation in the Pyeongchang Winter Olympics, there are also significant criticism and concerns both domestically and internationally,” the statement said.

During the visit, Kim Yo Jong had delivered a letter from her brother asking South Korean President Moon Jae-in to visit Pyongyang at his earliest convenience. Moon had replied, “Let’s create the environment for that to be able to happen,” according to the presidential Blue House.

Such a meeting, if it came about, would mark the first inter-Korea summit since 2007.

The two Koreas are still technically at war after the 1950-53 conflict on the Korean peninsula ended in a ceasefire and not a truce.

The Unification Ministry said steps regarding the improvement of ties would be led by the two Koreas, but also in cooperation with related countries and the support of the international community.

“We will fully cooperate with international efforts regarding sanctions against North Korea based on our stance for a denuclearised Korean peninsula and a peaceful solution (to the North Korea nuclear issue),” the statement said.

“If there is certain progress to set the conditions for denuclearisation, a full-fledged progress in inter-Korean relations will become possible,” it said, without elaborating.

In previous years, North and South Korea have held reunions to bring together family members who have been separated by the war.

Seoul made a standing offer to North Korea last year regarding another such reunion, details of which have yet to be hammered out between North and South Korea.

Kim Yo Jong and her delegation spent three days dining with top government officials, including Moon, watching the opening ceremony of the Pyeongchang Winter Olympics and cheering for the united women’s ice hockey team the two Koreas have fielded at this Olympics. (Reporting by Christine Kim; Editing by Lincoln Feast)